A334660 Dirichlet g.f.: 1 / zeta(s-4).

1, -16, -81, 0, -625, 1296, -2401, 0, 0, 10000, -14641, 0, -28561, 38416, 50625, 0, -83521, 0, -130321, 0, 194481, 234256, -279841, 0, 0, 456976, 0, 0, -707281, -810000, -923521, 0, 1185921, 1336336, 1500625, 0, -1874161, 2085136, 2313441, 0, -2825761, -3111696, -3418801, 0, 0, 4477456

Offset

1,2

Comments

Dirichlet inverse of A000583.

Moebius transform of A189922.

Inverse Moebius transform of A053826.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

G.f. A(x) satisfies: A(x) = x - 2^4 * A(x^2) - 3^4 * A(x^3) - 4^4 * A(x^4) - ...

a(1) = 1; a(n) = -n^4 * Sum_{d|n, d < n} a(d) / d^4.

a(n) = mu(n) * n^4.

Multiplicative with a(p^e) = -p^4 if e = 1 and 0 otherwise. - Amiram Eldar, Dec 05 2022

Mathematica

Table[MoebiusMu[n] n^4, {n, 46}]

Crossrefs

Cf. A008683, A055615, A334657, A334659.

Cf. A000583, A053826, A189922.

Sequence in context: A192510 A119508 A330480 * A088379 A005065 A056553

Adjacent sequences: A334657 A334658 A334659 * A334661 A334662 A334663

Keyword

sign,mult

Author

Ilya Gutkovskiy, May 07 2020

Status

approved